Mathematics - Vector Question with Solution | TestHub

The vectors $\bar{a},\bar{b}$ & $\bar{c}$ each two of which are non-collinear. If $\bar{a}+\bar{b}$ is collinear with $\bar{c},\bar{b}+\bar{c}$ is collinear with $\bar{a}\&|\bar{a}|=|\bar{b}|=|\bar{c}|=\sqrt{2}$. Then the value of $|\bar{a}\cdot \bar{b}+\bar{b}\cdot \bar{c}+\bar{c}\cdot \bar{a}|=$